Likely whoever is leaking the documents reached out to the WSJ since they’d have more cred in right wing circles. If the WSJ buried it, then the leaker would take it to another newspaper the story would still go out. Only difference would be the WSJ and Rupert Murdoch would be complicit in Trump’s cover up.

So it’s probably less Murdoch betraying Trump and more not wanting to go down with him. Plus it sells newspapers and Murdoch likes making money more than anything else.